Is the answer of the Handbook example 2.1 wrong?

[[email protected]]

Hi David,

This example is on page 33 of the sixth edition handbook. It's also the FRM exam 2009 question 2-3.

The question: The portfolio A's kurtosis is 1.9 and the analyst states it's more peaked than a normal dist.

The answer is b which says this statement is correct. I think this answer is wrong? Portfolio A is less peaked than normal because its kurtosis is less than 3.

Thanks in advance!!

 

[David Harper CFA FRM]

Hi handbookandbt,

Yes, I agree: the column header says "kurtosis" not "excess kurtosis" and kurtosis < 3 (i.e., Portfolio A kurtosis = 1.9) implies THINNER (less density in) tails which associates not with higher peaks but rather "stubbier" peaks (less peaked). In my view, the point about kurtosis (4th moment) is tail density, but in any case, it would be false to conclude "more peaked" here.

So, in my opinion, the answer should be (D): the analyst is incorrect on both statements (portfolio B with positive skew has a longer right tail)

Thanks, David

 

[[email protected]]

Thanks a lot for your quick reply!

 

[David Harper CFA FRM]

Sure thing, GARP just got back to us and confirmed:

"We went through our historical files and identified this question in the 2009 FRM examination where the correct answer choice was (D) and the brief explanation used to support (and the one provided to the publisher of the Handbook) was:

'The analyst’s statement is not correct in reference to either portfolio. Portfolio A has a kurtosis of less than 3 meaning that it is less peaked than a normal distribution (platykurtic). Portfolio B is positively skewed (long tail on the right side of the distribution).'

Thanks, David

 

[wshingw]

Sure thing, GARP just got back to us and confirmed:

"We went through our historical files and identified this question in the 2009 FRM examination where the correct answer choice was (D) and the brief explanation used to support (and the one provided to the publisher of the Handbook) was:

'The analyst’s statement is not correct in reference to either portfolio. Portfolio A has a kurtosis of less than 3 meaning that it is less peaked than a normal distribution (platykurtic). Portfolio B is positively skewed (long tail on the right side of the distribution).'

Thanks, David

Hi David,

Currently I am attending lesson from an institution, the lecturer was teaching the wrong concept as he is sticking with the 6th Handbook of GARP.

I attached a print screen of what he said to his student on FB.

I have been trying to get the reply from GARP but so far they did not give me any response.
I wonder if you could forward the email (from GARP) to me, the one that they replied to you?

Many many thanks if you could help.

Regards,
Davis

 

[David Harper CFA FRM]

Hi @wshingw

Sorry, I just checked but I received the email reply in 2011 and do not retain my emails that far back. But your instructor, with all due respect, is incorrect.

• There is really no such thing quite like an "official view:" unlike CFA which publishes a set of coherent references which could be used to arbitrate something like this, GARP's body of knowledge dynamically updates (with various authors) such that concepts are updated. There exist definitions in 2009 that would be wrong today, for example. As another example, the current econometric text has some errors; we wouldn't teach to the errors. Instead, we submit the errors and input the feedback to GARP. I don't think this is a bad thing, I rather prefer to think of this as realistic. Always seek the correct answer, regardless of who happens to be the current author. Authors make errors, the exam may contain an erroneous question (in which case, it will get identified because people will notice, don't worry!). Past exams definitely contain errors.
  
• But leptokurtosis (ie, kurtosis > 3 or excess kurtosis > 0) is clearly not "less peaked." That 2009 question contains a mistake, clearly. Kurtosis is a mathematical function, the standardized fourth moment about the mean. In terms of the FRM, the best "lazy" descriptor of high kurtosis, in my opinion, is "heavy tail" or "dense tail" or "fat tail" if you must (e.g., https://forum.bionicturtle.com/threads/kurtosis-and-peakedness.4758/#post-12546). It is also okay to say high kurtosis is associated with a higher peak compared to the normal, because this is almost always the case given the density predominates in the tail.
  
• The diagrams surely illustrate the student's t distribution. This is a well-known optical illusion because the illustrations tend to compare a standard normal (variance = 1) to a student's t with a higher variance. If you compare the student's t to a normal with same variance, the student's t will have a higher peak. So in will contribute to the vast majority of distributions that, when the tail is heavy, the peak is high. (It is my understanding that there do exist unimodal distributions with heavier tails and lower peaks, but they would be the exceptions not the rule. But, in any case, a focus on the peak misses the point. Kurtosis is about the tail). I hope that helps, thanks!

 

[wshingw]

Hi @wshingw

Sorry, I just checked but I received the email reply in 2011 and do not retain my emails that far back. But your instructor, with all due respect, is incorrect.

• There is really no such thing quite like an "official view:" unlike CFA which publishes a set of coherent references which could be used to arbitrate something like this, GARP's body of knowledge dynamically updates (with various authors) such that concepts are updated. There exist definitions in 2009 that would be wrong today, for example. As another example, the current econometric text has some errors; we wouldn't teach to the errors. Instead, we submit the errors and input the feedback to GARP. I don't think this is a bad thing, I rather prefer to think of this as realistic. Always seek the correct answer, regardless of who happens to be the current author. Authors make errors, the exam may contain an erroneous question (in which case, it will get identified because people will notice, don't worry!). Past exams definitely contain errors.
  
• But leptokurtosis (ie, kurtosis > 3 or excess kurtosis > 0) is clearly not "less peaked." That 2009 question contains a mistake, clearly. Kurtosis is a mathematical function, the standardized fourth moment about the mean. In terms of the FRM, the best "lazy" descriptor of high kurtosis, in my opinion, is "heavy tail" or "dense tail" or "fat tail" if you must (e.g., https://forum.bionicturtle.com/threads/kurtosis-and-peakedness.4758/#post-12546). It is also okay to say high kurtosis is associated with a higher peak compared to the normal, because this is almost always the case given the density predominates in the tail.
  
• The diagrams surely illustrate the student's t distribution. This is a well-known optical illusion because the illustrations tend to compare a standard normal (variance = 1) to a student's t with a higher variance. If you compare the student's t to a normal with same variance, the student's t will have a higher peak. So in will contribute to the vast majority of distributions that, when the tail is heavy, the peak is high. (It is my understanding that there do exist unimodal distributions with heavier tails and lower peaks, but they would be the exceptions not the rule. But, in any case, a focus on the peak misses the point. Kurtosis is about the tail). I hope that helps, thanks!

Hi David,

Thank you for the swift and detailed reply!